Abstract
Previously, we generalized the Lagrange polynomial interpolation at Chebyshev nodes and studied the Lagrange polynomial interpolation at a special class of sets of nodes. This special class includes some well-known sets of nodes, such as zeros of the Chebyshev polynomials of first and second kinds, Chebyshev extrema, and equidistant nodes. In this paper, we view our previous work from a different perspective and further generalize and study the Lagrange polynomial interpolation at a larger class of sets of nodes. In particular, the set of optimal nodes is included in this extended class.
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Acknowledgements
Professor Ward Cheney introduced me to the problem of optimal Lagrange polynomial interpolation. We have been working on this problem for many years. His advice and insights have been vital to the success of this project. I am very grateful to him for carefully reading different versions of this paper and making valuable suggestions. My appreciation is extended to Professor Larry Schumaker whose advice makes this paper much better.
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Chen, D. (2012). Generalization of Polynomial Interpolation at Chebyshev Nodes. In: Neamtu, M., Schumaker, L. (eds) Approximation Theory XIII: San Antonio 2010. Springer Proceedings in Mathematics, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0772-0_3
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DOI: https://doi.org/10.1007/978-1-4614-0772-0_3
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